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|Title:||Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems|
|Source:||Pang, J.-S.,Sun, D.,Sun, J. (2003). Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems. Mathematics of Operations Research 28 (1) : 39-63. ScholarBank@NUS Repository.|
|Abstract:||Based on an inverse function theorem for a system of semismooth equations, this paper establishes several necessary and sufficient conditions for an isolated solution of a complementarity problem defined on the cone of symmetric positive semidefinite matrices to be strongly regular/stable. We show further that for a parametric complementarity problem of this kind, if a solution corresponding to a base parameter is strongly stable, then a semismooth implicit solution function exists whose directional derivatives can be computed by solving certain affine problems on the critical cone at the base solution. Similar results are also derived for a complementarity problem defined on the Lorentz cone. The analysis relies on some new properties of the directional derivatives of the projector onto the semidefinite cone and the Lorentz cone.|
|Source Title:||Mathematics of Operations Research|
|Appears in Collections:||Staff Publications|
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